Frequency modulation continuous wave (FMCW)-based system for estimation and compensation of nonlinearity in linearly swept sources

Abstract

A frequency modulation continuous wave (FMCW)-based system configured to convert measurements of a linearly modulated wave from a time-domain into a frequency-domain to produce a non-linear frequency signal, where the non-linear frequency signal comprises a known linear component representing the desired linear modulation and an unknown non-linear component representing the non-linearity of the modulation. The FMCW-based system is further configured to determine coefficients of a basis function approximating a difference between the non-linear frequency signal and the linear frequency component in the frequency domain. The FMCW-based system is further configured to detect one or multiple spectrum peaks in the distorted beat signal with the distortion compensated according to the basis function with the determined coefficients to determine one or multiple distances to the one or multiple objects in the scene.

The invention claimed is: 
     
       1. A frequency modulation continuous wave (FMCW)-based system, comprising:
 an emitter configured to transmit at least one wave of radiation to a scene, wherein the transmitted wave is linearly modulated in a frequency domain, and wherein the linear modulation is subject to impairments causing a non-linearity of the transmitted wave in the frequency domain; 
 a receiver configured to receive a reflection of the transmitted wave from one or multiple objects in the scene; 
 a mixer operatively connected to the emitter and the receiver and configured to interfere a copy of the wave transmitted by the emitter with the reflection of the transmitted wave received by the receiver to generate a beat signal with spectrum peaks corresponding to reflections from the one or multiple objects in the scene, wherein the beat signal is distorted due to the non-linearity of the modulation caused by the impairments; 
 an analog-to-digital converter (ADC) operatively connected to the mixer and configured to generate samples of the distorted beat signal; 
 a frequency filter configured to pass signals at predetermined frequencies, the frequency filter is operatively connected to the emitter passing the linearly modulated wave transmitted by the emitter at different time instances at the predetermined frequencies to generate measurements of the modulated wave in a time-domain; and 
 at least one processor configured to:
 convert the measurements of the linearly modulated wave from the time-domain into a frequency-domain to produce a non-linear frequency signal, wherein the non-linear frequency signal comprises a known linear component representing the desired linear modulation and an unknown non-linear component representing the non-linearity of the modulation; 
 determine coefficients of a basis function approximating a difference between the non-linear frequency signal and the linear frequency component in the frequency domain; and 
 detect one or multiple spectrum peaks in the distorted beat signal with the distortion compensated according to the basis function with the determined coefficients to determine one or multiple distances to the one or multiple objects in the scene. 
 
 
     
     
       2. The FMCW-based system of  claim 1 , wherein a sampling frequency of the measurements of the linearly modulated wave produced by the frequency filter is 1000 times less than a sampling frequency of the ADC. 
     
     
       3. The FMCW-based system of  claim 1 , wherein the frequency filter includes an etalon producing an etalon signal, such that the samples in the time domain are peaks of the etalon signal at the different time instances making the samples in the time domain sparse. 
     
     
       4. The FMCW-based system of  claim 3 , wherein the processor is configured to:
 convert the etalon peaks into wavelengths based on a function of an index of each of the etalon peaks; and 
 convert the wavelengths into the non-linear frequency signal based on the base wavelength of the etalon and the order of etalon. 
 
     
     
       5. The FMCW-based system of  claim 4 , wherein the linear frequency signal is a linear function of time with a constant term of a center frequency at an etalon peak with the largest frequency change over all of the etalon peaks and a time coefficient of a relative frequency change over a time interval between two neighboring etalon peaks measured at two neighboring instances of time. 
     
     
       6. The FMCW-based system of  claim 5 , wherein to compensate the distortion in the distorted beat signal, the processor is configured to:
 maximize a cost function of a coherent summation of an approximation of a compensated distorted beat signal with parameters of the non-linear frequency signal including the determined coefficients of the basis function, the center frequency, and the time coefficient to produce a time delay estimation of the reflection of the transmitted wave; and 
 compensate the distorted beat signal based on the estimated time delay. 
 
     
     
       7. The FMCW-based system of  claim 1 , wherein the processor is configured to estimate the coefficients of the basis function by solving a least square problem to minimize the difference. 
     
     
       8. The FMCW-based system of  claim 7 , wherein the estimated coefficients of the basis function are a function of a polynomial component and peak time instants. 
     
     
       9. The FMCW-based system of  claim 1 , wherein to compensate for the distortion in the distorted beat signal, the processor is configured to:
 represent the non-linearity of the modulation caused by the impairments as a phase-domain nonlinearity function of the coefficients of the basis function and an unknown phase; and 
 compensate the distortion caused by the phase-domain nonlinearity function in a phase domain using a deskew-filtering approach. 
 
     
     
       10. A method, comprising:
 transmitting, by an emitter, at least one wave of radiation to a scene, wherein the transmitted wave is linearly modulated in a frequency domain, and wherein the linear modulation is subject to impairments causing a non-linearity of the transmitted wave in the frequency domain; 
 receiving, by a receiver, a reflection of the transmitted wave from one or multiple objects in the scene; 
 interfering, by a mixer, a copy of the transmitted wave with the received reflection of the transmitted wave to generate a beat signal with spectrum peaks corresponding to reflections from the one or multiple objects in the scene, wherein the beat signal is distorted due to the non-linearity of the modulation caused by the impairments; 
 generating, by an analog-to-digital converter (ADC), samples of the distorted beat signal; 
 passing, by a frequency filter, signals at predetermined frequencies, wherein the frequency filter is operatively connected to the emitter passing the linearly modulated wave transmitted by the emitter at different time instances at the predetermined frequencies to generate measurements of the modulated wave in a time-domain; 
 converting the measurements of the linearly modulated wave from the time-domain into a frequency-domain to produce a non-linear frequency signal, wherein the non-linear frequency signal comprises a known linear component representing the desired linear modulation and an unknown non-linear component representing the non-linearity of the modulation; 
 determining coefficients of a basis function approximating a difference between the non-linear frequency signal and the linear frequency component in the frequency domain; and 
 detecting one or multiple spectrum peaks in the distorted beat signal with the distortion compensated according to the basis function with the determined coefficients to determine one or multiple distances to the one or multiple objects in the scene. 
 
     
     
       11. The method of  claim 10 , wherein a sampling frequency of the measurements of the linearly modulated wave produced by the frequency filter is 1000 times less than a sampling frequency of the ADC. 
     
     
       12. The method of  claim 10 , wherein the frequency filter includes an etalon producing an etalon signal, such that the samples in the time domain are peaks of the etalon signal at the different time instances making the samples in the time domain sparse. 
     
     
       13. The method of  claim 12 , wherein the method further comprises:
 converting the etalon peaks into wavelengths based on a function of an index of each of the etalon peaks; and 
 converting the wavelengths into the non-linear frequency signal based on the base wavelength of the etalon and the order of etalon. 
 
     
     
       14. The method of  claim 13 , wherein the linear frequency signal is a linear function of time with a constant term of a center frequency at an etalon peak with the largest frequency change over all of the etalon peaks and a time coefficient of a relative frequency change over a time interval between two neighboring etalon peaks measured at two neighboring instances of time. 
     
     
       15. The method of  claim 14 , wherein for compensating the distortion in the distorted beat signal, the method further comprises:
 maximizing a cost function of a coherent summation of an approximation of a compensated distorted beat signal with parameters of the non-linear frequency signal including the determined coefficients of the basis function, the center frequency, and the time coefficient to produce a time delay estimation of the reflection of the transmitted wave; and 
 compensating the distorted beat signal based on the estimated time delay. 
 
     
     
       16. The method of  claim 10 , wherein the method further comprises estimating the coefficients of the basis function by solving a least square problem to minimize the difference. 
     
     
       17. The method of  claim 16 , wherein the estimated coefficient of the basis function is a function of a polynomial component and peak time instants. 
     
     
       18. The method of  claim 10 , wherein for compensating the distortion in the distorted beat signal, the method further comprises:
 representing the non-linearity of the modulation caused by the impairments as a phase-domain nonlinearity function of the coefficients of the basis function and an unknown phase; and 
 compensating the distortion caused by the phase-domain nonlinearity function in a phase domain using a deskew-filtering approach.